Bulletin of the
Korean Mathematical Society BKMS

Privacy preserving multiset union (PPMU) protocol allows a set of parties, each with a multiset, to collaboratively compute a multiset union {\em secretly}, meaning that any information other than union is not revealed. We propose efficient PPMU protocols, using multiplicative homomorphic cryptosystem. The novelty of our protocol is to directly encrypt a polynomial by representing it by an element of an extension field. The resulting protocols consist of constant rounds and improve communication cost. We also prove the security of our protocol against malicious adversaries, in the random oracle model.

Keywords: privacy preserving multiset union, ElGamal on polynomials, homomorphic encryption

MSC numbers: Primary 11T71, 68P25, 94A60